1. Field of the Invention
The present invention relates to a light-emitting semiconductor device with a quantum-wave interference layer which reflects carriers, i.e., electrons or holes, effectively, and with a quantum-wave interference layer which transmits carriers, i.e., electrons or holes, effectively. Especially, the present invention relates to a light-emitting semiconductor device such as a laser or a light-emitting diode with a structure which confines carriers in an emission layer so as to improve its luminous efficiency.
2. Description of the Related Art
A semiconductor device has been known to have a double hetero junction structure whose active layer is formed between n-type and p-type cladding layers. The cladding layers function as potential barriers for effectively confining carriers, or electrons and holes, within the active layer.
However, a problem persists in luminous efficiency. Carriers overflow the potential barriers of the cladding layers, which lowers luminous efficiency. Therefore, further improvement has been required, as presently appreciated by the present inventors.
As a countermeasure, forming cladding layers having a multiple quantum well structure of a first and a second layer as a unit in a laser diode in order to reflect carriers has been suggested by Takagi et al. (Japanese Journal of Applied Physics. Vol. 29, No.11, November 1990, pp.L1977-L1980). This reference, however, does not teach or suggest values of kinetic energy of carriers to be considered.
The inventor of the present invention conducted a series of experiments and found that, although it can be understood that Takagi et al. used a band gap energy alternative to a kinetic energy, the suggested thickness of the first and the second layers by Takagi et al. were too small to confine electrons, and that preferable thicknesses of the first and second layers are 4 to 6 times larger than those suggested by Takagi et al. So a problem still persisted in inadequacy of reflecting carriers.
Further, the present inventor thought that multiple quantum-wave reflection of carriers might occur by a multiple layer structure with different band width, like multiple light reflection by a dielectric multi-film structure. And the inventor thought that it would be possible to confine carriers by the reflection of the quantum-wave interference layer and filed an application with respect to this (Japanese Patent Application laid-open No. H10-303406).
Then the inventor of the present invention concerned a characteristic of electrons as a wave and considered that the quantum-wave interference layer functions as a transmission layer of carriers, by analogy with the multiple reflection of the light. That is, when each thickness of layers in the multiple layer structure is about an order of the wavelength of a quantum-wave of carriers, an interference effect of quantum-wave is considered to occur with respect to a conduction of carriers in the multiple layer structure. The interference effect caused a conduction as a wave. Accordingly, the inventor of the present invention considered that not a conduction of particle in a classical theory but a resonance of waves, an interference, or other phenomenon is occurred by an interference effect of electrons. This wave behavioral characteristic of electrons improves a mobility and a propagation velocity.
Then the inventor of the present invention combined a reflection layer and a transmission layer of carriers and formed an emission layer between the reflection layer and the transmission layer in a light-emitting semiconductor device. Accordingly, the inventor of the present invention obtained a light-emitting semiconductor device having a completely new structure.
It is, therefore, an object of the present invention is to provide a semiconductor device with a new structure, having both a quantum-wave interference layer with a large reflectivity to carriers which functions as a reflection layer and a quantum-wave interference layer with a high transmittivity and a high mobility to carriers which functions as a transmission layer.
In light of these objects a first aspect of the present invention is a light-emitting semiconductor device constituted by a first quantum-wave interference layer having plural periods of a pair of a first layer and a second layer, the second layer having a wider band gap than the first layer, a second quantum-wave interference layer having plural periods of a pair of a third layer and a fourth layer, the fourth-layer having a wider band gap than the third layer, and an emission layer formed between the first and the second quantum-wave interference layers. Each thickness of the first and the second layers in the first quantum-wave interference layer is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of carriers in each of the first and the second layers, each thickness of the third and the fourth layers in the second quantum-wave interference layer is determined by multiplying by an even number one fourth of a quantum-wave wavelength of carriers in each of the third and the fourth layers, and the thickness of the emission layer is determined by multiplying by an odd number one fourth of a quantum-wave wavelength of carriers in the emission layer. Here the emission layer formed between the first and the second quantum-wave interference layers may not contact to either the first or the second quantum-wave interference layers, or it may contact to both of the first and the second quantum-wave interference layers. Other semiconductor layers can exist at interfaces between the emission layer and the first quantum-wave interference layer and between the emission layer and the second quantum-wave interference layer.
A second aspect of the present invention is to form each thickness of the first and the second layers in the first quantum-wave interference layer by multiplying by an odd number one fourth of quantum-wave wavelength of carriers in each of the first and the second layers existing at the level near the lowest energy level of the second layer and to form each thickness of the third and the fourth layers in the second quantum-wave interference layer by multiplying an even number one fourth of quantum-wave wavelength of carriers in each of the third and the fourth layers existing at the level near the lowest energy level of the fourth layer. The thickness of the emission layer is determined by multiplying by an odd number one fourth of quantum-wave wavelength of carriers in the emission layer existing at the level near the lowest energy level of a layer which has a wider band gap and is adjacent to the emission layer. Here carriers transmit through the layer adjacent to the emission layer when the emission layer has a single layer structure, and when the emission layer has a single quantum well (SQW) structure or a multiple quantum well (MQW) structure, the layers adjacent to the emission layer are barrier layers formed on the both side of the emission layer.
A third aspect of the present invention is to form a xcex4R layer, which varies an energy band sharply, at an interface between the first and the second layers. A thickness of the xcex4R layer is substantially thinner than that of the first and the second layers.
A fourth aspect of the present invention is to form a xcex4T layer, which varies an energy band sharply, at an interface between the third and the fourth layers. A thickness of the xcex4T layer is substantially thinner than that of the third and the fourth layers.
A fifth aspect of the present invention is to define each thickness of the first and the second layers as follows:
DRW=nRWxcexRW/4=nRWh/4[2mRW(ER+VR)]xc2xdxe2x80x83xe2x80x83(1-1)
and
DRB=nRBxcexRB/4=nRBh/4(2mRBER)xc2xdxe2x80x83xe2x80x83(1-2)
In Eqs. 1-1 and 1-2, h, mRW, mRB, ER, VR, and nRW, nRB represent Plank""s constant, the effective mass of carriers in the first layer, the effective mass of carriers in the second layer, the kinetic energy of the carriers injected into the second layer, the potential energy of the second layer relative to the first layer, and odd numbers, respectively. Carriers injected into the second layer preferably exist around the lowest energy level of the second layer.
A sixth aspect of the present invention is to form a barrier layer between the first quantum-wave interference layer and the emission layer. The barrier layer has an enough thickness which is determined by multiplying an even number one fourth of quantum-wave wavelength of carriers transmitting in the barrier layer.
A seventh aspect of the present invention is to define each thickness of the third and the fourth layers as follows:
DTW=nTWxcexTW/4=nTWh/4[2mTW(ET+VT)]xc2xdxe2x80x83xe2x80x83(2-1)
and
DTB=nTBxcexTB/4=nTBhv/4(2mTBET)xc2xdxe2x80x83xe2x80x83(2-2)
In Eqs. 2-1 and 2-2, h, 2mTW, 2mTB, ET, VT and nTW, nTB represent Plank""s constant, the effective mass of carriers in the third layer, the effective mass of carriers in the fourth layer, the kinetic energy of the carriers injected into the fourth layer, the potential energy of the fourth layer relative to the third layer, and even numbers, respectively. Carriers injected into the fourth layer preferably exist around the lowest energy of the fourth layer.
An eighth aspect of the present invention is to form a barrier layer between the second quantum-wave interference layer and the emission layer. The barrier layer has an enough thickness which is determined by multiplying an even number one fourth of quantum-wave wavelength of carriers transmitting in the barrier layer.
A ninth aspect of the present invention is to determine the thickness of the emission layer DA which satisfies the formula:
DA=nAxcexA/4=nAh/4[2mA(EA+VA)]xc2xdxe2x80x83xe2x80x83(3)
In Eq. 3, h, mA, EA, VA, and nA represent Plank""s constant, the effective mass of carriers in the emission layer, the kinetic energy of the carriers injected into a layer which has a wider band gap and is adjacent to the emission layer, the potential energy of the layer which has a wider band gap and is adjacent to the emission layer relative to the emission layer, and an odd number, respectively. Carriers injected into the layer which is formed adjacent to the emission layer are preferably existing around the lowest energy of the emission layer. Here carriers transmit through the layer adjacent to the emission layer when the emission layer has a single layer structure. And when the emission layer has a single quantum well (SQW) structure or a multiple quantum well (MQW) structure, the layers adjacent to the emission layer are barrier layers formed on the both side of the emission layer.
A tenth aspect of the present invention is to provide the first quantum-wave interference layer which functions as a reflection layer of carriers and the second layer which functions as a transmission layer of carriers.
First, Second, Fifth, Seventh, Ninth, and Tenth Aspects of the Present Invention
The principle of the first quantum-wave interference layer of the present invention is explained hereinafter. FIG. 1 shows a conduction band of a multiple layer structure with plural periods of a first layer W and a second layer B as. a unit. A band gap of the second layer B is wider than that of the first layer W. Electrons conduct from left to right as shown by an arrow in FIG. 1. Among the electrons, those that exist at the level near the lowest energy level of a conduction band in the second layer B are most likely to contribute to conduction. The electrons near the bottom of conduction band of the second layer B has a kinetic energy E. Accordingly, the electrons in the first layer W have a kinetic energy E+V which is accelerated by potential energy V due to the band gap between the first layer W and the second layer B. In other words, electrons that move from the first layer W to the second layer B are decelerated by potential energy V and return to the original kinetic energy E in the second layer B. As explained above, kinetic energy of electrons in the conduction band is modulated by potential energy due to the multiple layer structure.
When thicknesses of the first layer W and the second layer B are equal to order of quantum-wave wavelength, electrons tend to have characteristics of a wave. The wave length of the electron quantum-wave is calculated by Eqs. 1-1 and 1-2 using kinetic energy of the electron. Further, defining the respective wave number vector of first layer W and second layer B as KW and KB, reflectivity R of the wave is calculated by:
R=(|KW51 xe2x88x92|KB|)/(|KW|+|KB|)
=[{mW(E+V)}xc2xd(mBE)xc2xd]/[{mW(E+V)}xc2xd+(mBE)xc2xd]
=[1xe2x88x92{mBE/mW(E+V)}xc2xd]/[1+{mBE/mW(E+V)}xc2xd]xe2x80x83xe2x80x83(4)
Further, when mB=mW, the reflectivity R is calculated by:
R=[1xe2x88x92{E/(E+V)}xc2xd]/[1+{E/(E+V)}xc2xd]xe2x80x83xe2x80x83(5).
When E/(E+V)=x, Eq. 5 is transformed into:
R=(1xe2x88x92xxc2xd)/(1+xxc2xd)xe2x80x83xe2x80x83(6).
The characteristic of the reflectivity R with respect to the energy ratio x obtained by Eq. 6 is shown in FIG. 2. And when each of the second layer B and the first layer W is laminated S times, the reflectivity RS of the quantum-wave incident facet is calculated by:
RS=[(1xe2x88x92xS)/(1+XS)]2xe2x80x83xe2x80x83(7)
When the condition xxe2x89xa60.1 is satisfied, Rxe2x89xa70.52. Accordingly, the relation between E and V is satisfied with:
Exe2x89xa6V/9xe2x80x83xe2x80x83(8).
Since the kinetic energy E of the conducting electrons in the second layer B exists near the bottom of the conduction band, the relation of Eq. 8 is satisfied and the reflectivity R at the interface between the second layer B and the first layer W becomes 52% or more. Consequently, the multiple quantum well layer structure can reflect quantum wave of electrons effectively.
Further, utilizing the energy ratio x enables the thickness ratio DB/DW of the second layer B to the first layer W to be obtained by:
DB/DW=[mW/(mBX)]xc2xdxe2x80x83xe2x80x83(9).
Thicknesses of the first layer W and the second layer B are determined for selectively transmitting one of holes and electrons, because of a difference in potential energy between the valence and the conduction bands, and a difference in effective mass of holes and electrons in the first layer W and the second layer B. Namely, the optimum thickness of the first and the second layers for reflecting electrons is not optimum for reflecting holes. Eqs. 1-1 and 1-2 refer to a structure of the quantum-wave interference layer for reflecting electrons selectively. The thickness for selectively reflecting electrons is designed based on a difference in potential energy of the conduction band and effective mass of electrons. Consequently, the quantum-wave interference layer has a high reflectivity for electrons, but not for holes.
Further, the thickness for selectively reflecting holes is designed based on a difference in potential energy of the valence band and effective mass of holes, realizing another type of quantum-wave interference layer which can reflect holes and transmits electrons.
The principle of the second quantum-wave interference layer of the present invention is explained hereinafter. When thicknesses of the third layer W and the fourth layer B are determined by multiplying an even number by one fourth of a quantum-wave wavelength, for example, a half of a quantum-wave wavelength, a standing wave rises in a quantum-wave interference layer, and a resonant conduction is occurred. That is, when a quantum-wave period of the standing wave and a potential period of the quantum-wave interference layer is corresponded to each other, a scattering of the carrier in each layer is suppressed, and a conduction of a high mobility is realized.
Thicknesses of the third layer W and the fourth layer B are determined for selectively transmitting one of holes and electrons, because of a difference in potential energy between the valence and the conduction bands, and a difference in effective mass of holes and electrons in the third layer W and the fourth layer B. Namely, the optimum thickness of the third and the fourth layers for transmitting electrons is not optimum for transmitting holes. Eqs. 2-1 and 2-2 refer to a structure of the quantum-wave interference layer for transmitting electrons selectively. The thickness for selectively transmitting electrons is designed based on a difference in potential energy of the conduction band and effective mass of electrons. Consequently, the quantum-wave interference layer has a high transmittivity (or a high mobility) for electrons, but not for holes.
Further, the thickness for selectively transmitting holes is designed based on a difference in potential energy of the valence band and effective mass of holes, realizing another type of quantum-wave interference layer as a hole-wave transmission layer, which has a high mobility for holes and which has an ordinary mobility for electrons.
Further explanation can be obtained by FIGS. 3A-3H. FIGS. 3A-3H illustrate the relationship between reflection of quantum-wave of electrons in a potential of quantum-well structure and a period of potential representing a conduction band of a multiple quantum well (MQW). FIGS. 3A-3D show the relationship when the period, i.e., width of the fourth layer B or the third layer W, of the potential is equal to an odd number multiplied by one fourth of the wavelength of propagated election quantum-wave. This type of the potential is named as xcex/4 type potential hereinafter. FIGS. 3E-3H show when the period of the potential is equal to a natural number multiplied by a half of the wavelength of propagated electron quantum-wave. This type of the potential is named as xcex/2 type potential hereinafter. In order to make it visually intelligible, thickness of each layers is unified in FIGS. 3A-3H. Electrons existing around the bottom of a conduction band of the fourth layer B conduct from left to right as shown by an arrow in FIGS. 3A and 3E. And in FIGS. 3B and 3F, the electrons reach the interface between the third layer W and the fourth layer B.
When the quantum-wave of the electrons reaches the interface between the fourth layer B and the third layer W in the xcex/4 type potential, a transmission wave QW2 and a reflection wave QW3 having a phase equal to that of the transmission wave QW2, are generated with respect to an incident wave QW1 as shown in FIG. 3C. Then when the transmission wave QW2 reaches the interface between the third layer W and the fourth layer B, a transmission wave QW4 and a reflection wave QW5 having a phase opposite to that of the transmission wave QW4 are generated as shown in FIG. 3D. The relationship between phases of the transmission wave and the reflection wave at the interface depends on falling or rising of a potential of the conduction band at the interface. In order to make it. visually intelligible, each amplitudes of QW1, QW2, QW3, QW4, and QW5 is unified in FIGS. 3A-3H.
With respect to the xcex/4 type potential of the multiple quantum well, the propagating quantum-wave of electrons represented by QW1, QW2 and QW4 and the reflecting quantum-wave of electrons represented by QW3 and QW5 cancels with each other, as shown in FIG. 3D. The quantum-wave of electrons represented by the QW1, QW2 and QW4 propagates from left to right, and the quantum-wave of electrons represented by the QW3 and QW5, generated by the reflection at two interfaces, propagates from right to left. Accordingly, a multiple quantum well, having a potential which is formed in a period, i.e., the width of the third layer W and the fourth layer B, determined by multiplying by an odd number one fourth of quantum-wave wavelength of propagated electrons, cancels the quantum-wave of electrons. In short, the multiple quantum well functions as a reflection layer which does not propagate electrons.
With respect to a multiple quantum well, having a potential which is formed in a period, i.e., the width of the third layer W and the fourth layer B, determined by multiplying by an even number one fourth of quantum-wave wavelength of propagated electrons, i.e., xcex/2 type potential, as shown in FIGS. 3E-3H, the quantum-wave of electrons can become a standing wave.
Similarly, when a quantum-wave of electrons reaches the interface between the fourth layer B and the third layer W in the xcex/2 type potential, a transmission wave QW2 and a reflection wave QW3 having a phase corresponding to that of the transmission wave QW2, are generated with respect to an incident wave QW1 as shown in FIG. 3G. Then when the transmission wave QW2 reaches the interface between the third layer W and the fourth layer B, a transmission wave QW4 and a reflection wave QW5 having a phase opposite to that of the transmission wave QW4 are generated as shown in FIG. 3H. With respect to xcex/2 type potential of the multiple quantum well, the propagating quantum-wave of electrons represented by QW1, QW2 and QW4 and the reflecting quantum-wave of electrons represented by QW5 intensifies to each other, as shown in FIG. 3H. On the other hand, the reflection waves QW3 and QW5 can be considered to cancel with each other and the quantum-wave of electrons which is propagated from left to right in FIG. 3E can be a standing wave. Accordingly, with respect to the multiple quantum well, having a potential which is formed in a period, i.e., the width of the third layer W and the fourth layer B, determined by multiplying by an even number one fourth of quantum-wave wavelength of propagated electrons, the quantum-wave of electrons can become a standing wave and a transmission layer having a high transmittivity (or a high mobility) for electrons can be realized.
Alternatively, a multiple quantum well, having a potential which is formed in a period determined by multiplying by a natural number half of quantum-wave wavelength of holes, can be applied to the relationship described above.
A quantum wave optimum to the emission layer is considered hereinbelow. When carriers transmit the emission layer, electron-hole pairs are generated after carriers pass the emission layer, which is not suitable for a light-emitting device. Stable existence of quantum wave may hinder from generating electron-hole pairs. Accordingly, an emission layer preferably has the same structure as either one of the reflection layer and a single layer structure so that it does not transmit quantum wave and in which quantum wave does not exist stably. When the emission layer has a single layer structure, its thickness is determined by multiplying by an odd number one fourth of a wavelength of carriers. When the emission layer has a multiple layer structure, its thickness is preferably determined by multiplying by an odd number one fourth of a wavelength of the layer which has a narrower band gap and which at least generates electron-hole pairs. Here the emission layer is a well layer which is substantially concerned in light emission.
Accordingly, a light-emitting semiconductor device, in which a pair of a first and a second quantum-wave interference layers to one of electrons and holes and an emission layer having a thickness determined by multiplying by an odd number one fourth of quantum-wave wavelength of carriers in the emission layer are formed, is obtained as described above is obtained. When electrons or holes are injected from the second-quantum-wave interference layer to the first quantum-wave interference layer, electrons or holes, which are not interrupted and flows with a high transmittivity in the second quantum-wave interference layer, reach the first quantum-wave interference layer and are reflected effectively, and electron-hole pairs, generated by instable existence of quantum waves in the emission layer, improves luminous efficiency of the device. Accordingly, a light-emitting semiconductor device in the present invention comprising a pair of a first and a second quantum-wave interference layer for electrons or holes and an emission layer enables to considerably improve the efficiency of the device compared with conventional semiconductor devices and has a completely new structure. A light-emitting semiconductor device comprising both a pair of a first and a second quantum-wave interference layers for electrons as carriers and an emission layer is more preferable.
Third and Fourth Aspects of the Present Invention
FIGS. 4-4D illustrate to form a xcex4R layer (disclosed as a xcex4 layer in FIGS. 4A-4D) at the interface between the first layer W and the second layer B. The xcex4R layer has a relatively thinner thickness than both of the first layer W and the second layer B and sharply varies an energy band. By sharply varying the band gap of the interfaces, the potential energy V of an energy band becomes larger substantially and the value x of Eq. 6 becomes smaller, as shown in FIGS. 4A-4D. This is shown in FIGS. 5A-5D. Without forming a xcex4R layer as shown in FIG. 5A, a part of component of the first layer W and the second layer B mixes when the second layer B is laminated on the first layer W, and an energy band gap which varies sharply cannot be obtained, as shown in FIG. 5B. When a xcex4R layer is formed at each interfaces of the first and the second layers as shown in FIG. 5C, even if a part of component of the first layer W and the second layer B mixes, an energy band gap varies sharply compared with the case without xcex4R layers, as shown in FIG. 5D.
Variations are shown in FIGS. 4A to 4D. The xcex4R layer may be formed on both ends of the every first layer W as shown in FIGS. 4A to 4D. In FIG. 4A, the xcex4R layers are formed so that an energy level higher than that of the second layer B may be formed. In FIG. 4B, the xcex4R layers are formed so that a band having lower bottom than that of the first layer W may be formed. In FIG. 4C, the xcex4R layers are formed so that the energy level higher than that of the second layer B and the energy level lower than that of the first layer W may be formed. As an alternative to the variation shown in FIG. 4C, the xcex4R layer can be formed on only either one end of every layer as shown in FIG. 4D.
A xcex4T layer can be formed at the interface between the third layer W and the fourth layer B. The xcex4T layer which has a relatively thinner thickness than both of the third layer W and the fourth layer B and sharply varies an energy band has the same effect as that of the xcex4R layer formed at the interface between the first layer W and the second layer B. The xcex4T layer may be formed in one of a plural quantum-wave interference layers or may be formed in all of the layers.
Sixth and Eighth Aspects of the Present Invention
By forming an enough thickness of barrier layer between the first quantum-wave interference layer and the emission layer, carriers are effectively accumulated in the emission layer. The thickness of the barrier layer is preferably determined by multiplying by an even number one fourth of quantum-wave wavelength of carriers from consideration shown in FIGS. 3A-3H. If the thickness of the barrier layer is determined by multiplying by an odd number one fourth of quantum-wave wavelength of carriers, the barrier layer only reflects carriers and does not inject carriers into the emission layer. Similarly, by forming an enough thickness of barrier layer between the second quantum-wave interference layer and the emission layer, carriers are effectively accumulated in the emission layer. The thickness of the barrier layer is preferably determined by multiplying by an even number one fourth of quantum-wave wavelength of carriers.
FIG. 6 illustrates the structure of forming the barrier layers between the first quantum-wave interference layer and the emission layer and between the second quantum-wave interference layer and the emission layer. Electrons, which function as carriers, conduct from the second quantum-wave interference layer, pass through the emission layer and to the first quantum-wave interference layer. The second quantum-wave interference layer has a thickness determined by multiplying by a half of a quantum-wave wavelength of electrons, and comprises a third and a fourth layers. A barrier layer twice as thick as a quantum-wave wavelength of electrons is formed between the second quantum-wave interference layer and the emission layer. The emission layer has a thickness three-fourths of a quantum-wave wavelength of electrons. A barrier layer twice as thick as a quantum-wave wavelength of electrons is formed between the emission layer and the first quantum-wave interference layer. The first quantum-wave interference layer has a thickness determined by multiplying by one fourth of a quantum-wave wavelength of electrons, and comprises a first and a second layers.
When electrons conduct from the second quantum-wave interference layer to the emission layer, the barrier layer formed between the second quantum-wave interference layer and the emission layer may not reflect but can transmit electrons because it has a thickness twice as large as that of a quantum-wave wavelength of electrons. Then electrons conduct from the emission layer to the first quantum-wave interference layer. Because the barrier layer formed between the emission layer and the first quantum-wave interference layer has a thickness twice as large as a quantum-wave wavelength of electrons, electrons are not reflected by the barrier layer but may be reflected by the first quantum-wave interference layer. Electrons reflected by the first quantum-wave interference layer then transmit the barrier layer having a thickness twice as large as that of a quantum-wave wavelength of electrons and reach the emission layer again. Because the emission layer has a thickness three-fourths of a quantum-wave wavelength of electrons, a quantum-wave of electrons does not become a standing wave but tends to product pairs with holes. Here the emission layer is a well layer substantially concerned in light emission. When the emission layer has a multiple quantum well structure, each well layers functions as an emission layer and barrier layers formed on both sides of layers in the emission layer are the above-described barrier layers.
As another example, as shown in FIG. 7, a plurality of partial quantum-wave interference layers IRk as the first quantum-wave interference layer, the first electron-wave interference layer or the first hole-wave interference layer may be formed corresponding to each of a plurality of kinetic energy levels ERk. Each of the partial quantum-wave interference layers IRk has TRk periods of a first layer W and a second layer B as a unit whose respective thicknesses (DRWk, DRBk) are determined by following Eqs. 10-1 and 10-2. The plurality of the partial quantum-wave interference layer IRk is arranged in series with respect to the number k of kinetic energy levels ERk.
DRWk=nRWkxcexRWk/4=nRWkh/4[2mRWk(ERk+VR)]xc2xdxe2x80x83xe2x80x83(10-1)
and
DRBk=nRBkxcexRBk/4=nRBkh/4(2mRBkERk)xc2xdxe2x80x83xe2x80x83(10-2)
That is, the quantum-wave interference layer is formed by a serial connection of IR1, IR2, . . . and IRj. As shown in FIG. 7, electrons with each of the kinetic energy levels ERk are reflected by the corresponding partial quantum-wave interference layers IRj. Accordingly, electrons belonging to each of the kinetic energy levels from ER1 to ERj are reflected effectively. By designing the intervals between the kinetic energies to be short, thicknesses of the first layer W and the second layer B (DRWk, DRBk) in each of the partial quantum-wave interference layers IRk vary continuously with respect to the value k. Similarly, a plurality of partial quantum-wave interference layers ITk may be formed corresponding to each of a plurality of kinetic energy levels ETk. Each of the partial quantum-wave interference layers ITk has TTk periods of a first layer W and a second layer B as a unit whose respective thicknesses (DTWk, DTBk) are determined by following Eqs. 11-1 and 11-2. The plurality of the partial quantum-wave interference layer ITk is arranged in series with respect to the number k of kinetic energy levels ETk. That is, the quantum-wave interference layer is formed by a serial connection of IT1, IT2, . . . , and ITj. This quantum-wave interference layer becomes to have a high transmittivity (or a high mobility) with carriers.
DTWk=nTWkxcexTWk/4=nTWkh/4[2mTWk(ETk+VT)]xc2xdxe2x80x83xe2x80x83(11-1)
and
DTBk=nTBkxcexTBk/4=nTBkh/4(2mTBkETk)xc2xdxe2x80x83xe2x80x83(11-2)
As shown in FIG. 8, a plurality of partial quantum-wave interference layers may be formed with an arbitrary period as the first quantum-wave interference layer, the first electron-wave interference layer or the first hole-wave interference layer. Each of the partial quantum-wave interference layers IR1, IR2, . . . is made of serial pairs of the first layer W and the second layer B with widths (DRWk, DRBk) determined by Eqs. 10-1 and 10-2. That is, the partial quantum-wave interference layer, e.g., IR1, is constructed with serial layers of width (DRW1, DRB1), . . . , (DRWk, DRBk), . . . , (DRWj, DRBj) . A plurality IR1, IR2, . . . of layers such as IR1 are connected in series to form the total quantum-wave interference layer. Accordingly, electrons of the plurality of kinetic energy levels ERk are reflected by each pair of layers in each partial quantum-wave interference layers. By designing the intervals between kinetic energies to be short, thicknesses of the pair of the first layer W and the second layer B (DRWk, DRBk) in a certain partial quantum-wave interference layer IRk varies continuously with respect to the value k. Similarly, a plurality of partial quantum-wave interference layers, each of which is made of serial pairs of the first layer W and the second layer B with widths (DTWk, DTBk) determined by Eqs. 11-1 and 11-2, may be formed with an arbitrary period as the second quantum-wave interference layer, the second electron-wave interference layer or the second hole-wave interference layer. That is, the partial quantum-wave interference layer is constructed with serial layers of width (DTW1, DTB1) , . . . , (DTWk, DTBk), . . . , (DTWj, DTBj). This quantum-wave interference layer becomes to have a high transmittivity (or a high mobility) with carriers.